{"title":"Generalized spherical principal component analysis","authors":"Sarah Leyder, Jakob Raymaekers, Tim Verdonck","doi":"10.1007/s11222-024-10413-9","DOIUrl":null,"url":null,"abstract":"<p>Outliers contaminating data sets are a challenge to statistical estimators. Even a small fraction of outlying observations can heavily influence most classical statistical methods. In this paper we propose generalized spherical principal component analysis, a new robust version of principal component analysis that is based on the generalized spatial sign covariance matrix. Theoretical properties of the proposed method including influence functions, breakdown values and asymptotic efficiencies are derived. These theoretical results are complemented with an extensive simulation study and two real-data examples. We illustrate that generalized spherical principal component analysis can combine great robustness with solid efficiency properties, in addition to a low computational cost.</p>","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics and Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11222-024-10413-9","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
Outliers contaminating data sets are a challenge to statistical estimators. Even a small fraction of outlying observations can heavily influence most classical statistical methods. In this paper we propose generalized spherical principal component analysis, a new robust version of principal component analysis that is based on the generalized spatial sign covariance matrix. Theoretical properties of the proposed method including influence functions, breakdown values and asymptotic efficiencies are derived. These theoretical results are complemented with an extensive simulation study and two real-data examples. We illustrate that generalized spherical principal component analysis can combine great robustness with solid efficiency properties, in addition to a low computational cost.
期刊介绍：
Statistics and Computing is a bi-monthly refereed journal which publishes papers covering the range of the interface between the statistical and computing sciences.
In particular, it addresses the use of statistical concepts in computing science, for example in machine learning, computer vision and data analytics, as well as the use of computers in data modelling, prediction and analysis. Specific topics which are covered include: techniques for evaluating analytically intractable problems such as bootstrap resampling, Markov chain Monte Carlo, sequential Monte Carlo, approximate Bayesian computation, search and optimization methods, stochastic simulation and Monte Carlo, graphics, computer environments, statistical approaches to software errors, information retrieval, machine learning, statistics of databases and database technology, huge data sets and big data analytics, computer algebra, graphical models, image processing, tomography, inverse problems and uncertainty quantification.
In addition, the journal contains original research reports, authoritative review papers, discussed papers, and occasional special issues on particular topics or carrying proceedings of relevant conferences. Statistics and Computing also publishes book review and software review sections.
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